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SparseMatrix does not contain a definition 'LU'

Nov 15, 2013 at 12:57 PM
Edited Nov 15, 2013 at 2:49 PM
Hi to all,

I am having a problem with the solvers provided in MathNet. Let me explain what I am trying to do, I have a very big non-square sparse matrix (five non-zeroes per row), of a size of 20,000x12,000, and I would like to solve it with the least squares method, but I am stucked.

I could prepare the matrix to solve it with a direct solver like LUby setting some fixed values and getting a square matrix and some other things (it is the way I was trying to implement). But, how can I solve this system by least squares method? Can I do it without any pre-processing directly over the Mx = b system?

I have this variables:
MathNet.Numerics.LinearAlgebra.Double.SparseMatrix M = new MathNet.Numerics.LinearAlgebra.Double.SparseMatrix(m,n, 0.0);

//I populate the matrix with the .SetRow method

MathNet.Numerics.LinearAlgebra.Double.DenseVector b = new MathNet.Numerics.LinearAlgebra.Double.DenseVector(m); //b is all zeroes.
But when I try to solve it (directly, without preparing it, just to see what happens):
MathNet.Numerics.LinearAlgebra.Double.DenseVector result = M.LU().Solve(b);
It appears a message saying that SparseMatrix does not contain a definition called LU or an extension method called like that...

I have tried to define the matrixv M as a DenseMatrix, but I get an OutOfMemory exception, but defining a smaller DenseMatrix I get the same message...

What is happening? I do not know to use the solvers, any help?

Thanks in advanced!
Nov 15, 2013 at 10:49 PM
Edited Nov 15, 2013 at 11:11 PM

While it is technically possible to go for a direct solver/factorization, for a matrix of this size (~1.8 GB) this is currently only feasible in practice (if at all) when using our native MKL provider and an actual dense matrix (not sparse, since it will perform badly - this is something we hope to adress for the v3 release though).

I assume the "message" you see is actually a compilation error? In V2, LU() was indeed defined in an extension method so you may be missing its namespace. However, in V3 this is a proper method.

However, you may want to give the iterative sparse solvers a trial, especially with the new MILU0 preconditioner in v3.0.0-alpha5:

NuGet packages: MathNet.Numerics v3.0.0-alpha5, MathNet.Numerics.Data.Text v3.0.0-alpha5
Namespaces: MathNet.Numerics.Data.Text, MathNet.Numerics.LinearAlgebra, MathNet.Numerics.LinearAlgebra.Double, MathNet.Numerics.LinearAlgebra.Double.Solvers, MathNet.Numerics.LinearAlgebra.Solvers

I'm using a matrix from NIST MatrixMarket here, which is 1633x1633, 1.75% non-zero, and compute a b vector (that's why I'm also using the .Data.Text package here, you won't need it in your case). But it works also well e.g. with UTM5940 which is a bit larger, 5940x5940, 0.24% non-zero. Both should converge in less than 10-20ms.
// m is Matrix<double> but its value is actually of type Double.SparseMatrix
var m = MatrixMarketReader.ReadMatrix<double>(@"fidap007.mtx");
var b = m * DenseVector.Create(m.RowCount, 1.0);
var solver = new BiCgStab();
var preconditioner = new MILU0Preconditioner();
var iterator = new Iterator<double>(
    new ResidualStopCriterium(1.0e-8),
    new IterationCountStopCriterium<double>(1000));

var x = m.SolveIterative(b, solver, iterator, preconditioner);
var status = iterator.Status;
However, how well this works depends on your data. You may need to tweak the parameters a bit, the stop criteria, preconditioner, or try a solver other than BiCgStab.

Marked as answer by cdrnet on 12/31/2013 at 1:44 AM